Holographic direct view display having an apodization device

ABSTRACT

The invention relates to apodization in a holographic direct view display. Known apodization functions are utilized/modified for an apodization mask such that the functions reduce the intensities of selected higher magnitudes of diffractions. The holographic direct view display comprises a controllable light modulator having modulator cells and modulating impinging coherent light into a phase and/or amplitude, and an array of apodization masks. The apodization masks have the same apodization function for a predetermined group of modulator cells, by means of which function a complex amplitude transparency can be set for the modulator cells. This transparency corresponds to an individually predefined course of intensity in a far field of the light modulator, wherein the predefined course of intensity includes a reducing of the light intensity of higher magnitudes of diffractions, and/or of the interfering light emitted by the light modulator.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the priority of PCT/EP2009/050476, filed on Jan.16, 2009, which claims priority to German Application No. 10 2008002692.1, filed Jun. 26, 2008, the entire contents of which are herebyincorporated in total by reference.

BACKGROUND OF THE INVENTION

The present invention relates to a holographic direct-view display whichcomprises at least one controllable spatial light modulator with amatrix of modulator cells for diffracting light and an array ofapodisation masks. Further, this invention relates to an iterativeprocess for finding an apodisation function for apodisation masks.

The field of application of this invention includes opto-electronicdisplay devices which shall have a large display area and/or littlestructural depth, such as direct-view displays for PC, TV, mobiletelephones or other appliances with the function of displayinginformation.

The matrix of modulator cells of a controllable spatial light modulator(SLM) comprises actively switchable modulator regions and inactiveregions in between (division bars, cell boundaries). The area ratio ofthese two regions is known as fill factor. The inactive regions form afixed grating structure at which light is diffracted. The diffractedlight will show characteristic multi-beam interference effects if thespatial light modulator is illuminated with coherent or partly coherentlight. The diffraction far field of a spatial light modulatorcorresponds with the Fourier transform of the complex amplitudetransmission or complex amplitude reflection of the spatial lightmodulator. The inactive regions are predefined and characteristic foreach type of SLM. At these regions the diffraction causes higherdiffraction orders to occur, which can be to the detriment of thefunctionality and quality of an optical system.

If they are superposed on the actual image of the holographicreconstruction, higher diffraction orders can for example adverselyaffect the functionality of optical systems in the form of increasednoise, twin images or e.g. by bright spots around the image points ofthe SLM which are generated in the far field. An efficient means forblanking out higher diffraction orders, which are caused by themodulator cells of the SLM matrix, which is known in the prior art arespatial filters which are disposed in an intermediate focal point of theoptical system which follows the SLM. The spatial filter only transmitsthe desired diffraction order while all other diffraction orders areblocked by the spatial filter, which is designed as an aperture mask. Adisadvantage of such a filter arrangement is that an intermediate imageor an intermediate focus must be created following the SLM in theoptical path. First, this considerably increases the structural depth ofthe optical system. Secondly, the aperture (effective opening) of thesubsequent optical system (a lens or mirror) must be about as large asthat of the SLM. This limits the applicability of such spatial filtersto relatively small SLM and thus to projection-type displays.

Apodisation is a method for optical filtering where the outer rings ofan Airy disc, which represent the higher orders, are suppressed.Advantage is taken of this method for example in imaging systems forimproving the image contrast at the expense of the resolution of imagingsystems, in that for example a special gradient filter is disposed inthe exit aperture of the optical path.

The apodisation of modulator cells can be achieved with the help of anapodisation function t_(SLM pixel) (x,y). Generally, apodisationfunctions are computed in accordance with their actual usage, andrealised e.g. in a mask or filter. Further, a number of knownapodisation functions which can be described analytically are discussedin the literature. In addition to a cosine or triangular function, thereare for example apodisation functions which are known under the names ofBlackman, Hamming, or Welch functions. These apodisation functions offersolutions for general apodisation tasks.

Document DE 10 2006 030 535 A1 filed by the applicant describes the useof apodisation functions in spatial light modulators with a pixel matrixin a projection display. The apodisation of the pixel matrix is hereachieved exclusively by a respective modulation of the light whichilluminates the spatial light modulators. For this, a plane coherentillumination wave is modulated with a suitable function whoseperiodicity is matched to the pixel structure of the modulators.

In a holographic direct-view display for generating a holographicreconstruction, the controllable light modulator is illuminated withsufficiently coherent light and generates a separate visibility region(also known as observer window) for each eye in the far field. Theintensities of the higher diffraction orders can be emitted into theneighbouring visibility region and thus disturb the observer whenwatching the reconstruction. There are hitherto no known solutions basedon apodisation which serve to reduce cross-talking of higher diffractionorders among these visibility regions.

As is generally known, to become effective, apodisation must satisfy theboundary conditions which are given by the actually used light modulatormeans.

Summarising, the prior art exhibits the following deficiencies. For thegeneration of a true holographic reconstruction, where the brightnessvalues are represented as realistic as possible, it is required thathigher diffraction orders are specifically reduced in at least onecertain region. These regions lie at a defined position in the observerplane. In particular, it shall be possible to reduce particularlygreatly those diffraction orders which fall into the other eye.

Another application which is not realised with conventional apodisationfunctions is the increase of the relative luminous intensity in at leastone diffraction order other than the zeroth order relative to all otherdiffraction orders.

SUMMARY OF THE INVENTION

It is the object of the present invention to reduce by way of anapodisation the higher diffraction orders caused by the modulator cellsin the far field of a controllable spatial light modulator of aholographic direct-view display which comprises a matrix of controllablemodulator cells, where the light modulator is a component of an opticalsystem which does not permit filtering by a spatial filter.

The problems shall be eliminated with the help of an array ofapodisation masks. The light modulator shall also allow an individualspecification of the intensity distribution in different diffractionorders of diffracted coherent light.

At the same time, other disturbing effects which are caused by thedesign of the modulator cells shall also be eliminated as far aspossible so to improve the imaging quality of the optical system.

Further, it shall be possible either to give the apodisation function acontinuous profile or to realise an apodisation function with discretevalues of individual steps across the modulator cell in the apodisationmask.

Further, known apodisation functions shall generally be modified suchthat these modifications are valid for different applications and aretechnologically feasible.

The transmittance of the holographic direct-view display shall therebyonly be reduced to a very small degree.

The object is solved according to this invention by a holographicdirect-view display, comprising

-   -   At least one controllable spatial light modulator comprising a        matrix of modulator cells for diffracting light, said spatial        light modulator realising an individually predefined intensity        profile in the far field of the light modulator,    -   An array of apodisation masks, where each modulator cell for        modulating the phase and/or amplitude of sufficiently coherent        light is assigned to an apodisation mask,    -   At least one defined group of modulator cells which are assigned        to apodisation masks with an identical apodisation function, and    -   A complex amplitude transparency which is to be set for the at        least one group of modulator cells and which sets the        apodisation function for this group of modulator cells according        to the predefined intensity profile which is to be realised,        where the predefined intensity profile includes a reduction of        the luminous intensity in at least one higher diffraction order        and/or of the stray light which is emitted by the light        modulator.

Complex amplitude transparency is understood in this context as acomplex-valued filtering function T which has an amplitude A and a phaseφ in the form T (x,y)=A (x,y)·exp [iφ (x,y)].

It describes the change in amplitude and phase of an electromagneticwave which runs through the apodisation mask.

In an embodiment of the present invention, the apodisation function ofan apodisation mask exhibits at least in one dimension a non-constantprofile of the absolute value and/or phase of the complex amplitudetransparency. For example, the apodisation function can at least in onedimension have a maximum in the centre of a modulator cell, and agradually decreasing complex amplitude transparency towards the edges ofa modulator cell.

To be able to compute the apodisation function, the given shape, sizeand geometry and an already inherent complex amplitude transparency of amodulator cell which is to be apodised must be known. In particular, itis essential to know the parameters pixel pitch, fill factor, and shapeand position of the pixel aperture. If the fill factor FF of a singlemodulator cell is for example FF>0.5, and if the area of the modulatorcell is not too small, then a specific selection of the transmittanceprofile of the individual modulator cell serves to achieve thatintensities of higher diffraction orders of an observer window do notcross-talk to the observer window of the neighbouring eye in adisturbing manner.

The apodisation function is defined at discrete scan points by numericalvalues which describe the complex amplitude transparency at those scanpoints, where the scan points exhibit a mutual distance which can bespatially resolved by the apodisation mask.

In one embodiment of the holographic direct-view display, at least twocontrollable light modulators are sandwiched together, where either eachlight modulator has a dedicated apodisation mask or the at least twolight modulators have a common apodisation mask.

Further, one light modulator of the at least two controllable lightmodulators of the holographic direct-view display is designed to form aprism array which comprises electrowetting cells. It is provided thatthe apodisation masks are assigned to the prism array of electrowettingcells or combined with the latter. The location of the array ofapodisation mask in the holographic direct-view display is not firmlydefined.

The apodisation masks of the given group of modulator cells canpreferably set an intensity profile with predefined intensity values ina given section of the far field of the diffracted light. The givensection of the far field can comprise either only negative or onlypositive diffraction orders in at least one dimension.

It is further possible that all modulator cells have the sameapodisation function for one application.

In a further embodiment of the invention, the holographic direct-viewdisplay for 3D presentations is designed such that the modulator cellsare assigned in given groups always to a left and to a right observereye for generating visibility regions which are respectively assigned tothe observer eyes in an observer distance range to the light modulator.In the apodisation masks of the one group, the intensity profile is setsuch that it is minimised at the observer eye of the other group andvice versa.

Further, the apodisation masks can exhibit an apodisation function whosecomplex amplitude transparency is formed as a variable phase functionwith constant absolute value. According to another embodiment, theapodisation mask exhibits an apodisation function whose complexamplitude transparency is of a binary type, so to reduce preferablystray light. In combination with an electrowetting cell, a binaryapodisation mask is a suitable element for minimising phase defectswhich occur at the margin of this cell.

Further, an array of binary masks can artificially reduce the fillfactor of the array of electrowetting cells if a certain apodisationfunction is preferably used for which that fill factor is sensible.

For precisely determining the apodisation function, an iterative processcan be used which is run as a computing routine in a computing unitwhich provides the result in a memory unit for being retrieved.

The iterative process is based for example on a Fourier transformationmethod where the transform is carried out between the plane of the lightmodulator and its Fourier plane in the far field. The light which isdiffracted at the modulator cells can be approximated to given intensityvalues in the given section of the far field.

The holographic direct-view display can comprise an array ofamplitude-only masks or phase-only masks as apodisation masks. Theamplitude masks can be manufactured for example by way ofprojection-lithographic, interference-lithographic orgreyscale-lithographic methods. For this, a photosensitive material,such as a holographic film, is exposed where the function is exposedpoint-wise or two-dimensionally. Alternatively, it is possible torealise a direct exposure in high-energy beam sensitive (HEBS) glass byan electron beam or in laser direct write (LDW) glass by a laser beam.Yet another manufacturing option is digital printing.

The phase masks can be made by generating surface profiles or by way ofrefractive index modulation in polymers or glass. A photosensitivematerial (e.g. photoresist) is exposed for this as well. The informationis written to the material two-dimensionally, so that an array ofapodisation masks can be realised by adjoining multiple areal regions.Alternative manufacturing options include areal contact or proximityexposure and projection lithography, where again multiple regions can beadjoined to form an array of apodisation masks. Yet another possibilityof manufacturing is the local ion exchange by the implantation oflithium ions in glass substrates.

The above-mentioned methods also allow amplitude masks to be transformedinto phase masks.

The masks can also be manufactured with the help of methods which arenot mentioned above, but whose usage would be considered appropriate bya person skilled in the art.

In another embodiment, the holographic direct-view display can be aholographic colour display in which the modulator cells which are to beassigned to a certain primary colour form a given group. In order tominimise the intensity values, in such a display the given section ofthe far field includes a region of identical diffraction angles for allprimary colours.

The present invention further relates to a method for finding anapodisation function for apodisation masks which are arranged in anarray and which are assigned to a matrix of modulator cells of acontrollable spatial light modulator, where the method is carried out initerative process steps.

The process steps are in detail:

-   -   Determining the position of diffraction orders of the modulator        cells of a given group,    -   Definition of an individually predefined intensity profile in        preferred diffraction orders or sections thereof in the far        field,    -   Definition of an initial apodisation function for a single        modulator cell of the given group, and    -   Stepwise optimisation of the complex amplitude transparency of        the apodisation function to approximate to the predefined        intensity profile in the preferred diffraction orders of        sections thereof in the far field.

In order to determine the complex amplitude transparency of a modulatorcell, a number of scan points inside and outside the aperture of themodulator cell is defined. Further, the intensity profile in the farfield is determined by the square absolute value of the Fouriertransform of the complex amplitude transparency at an identical numberof scan points. After that, the stepwise optimisation of the complexamplitude transparency of the apodisation function takes place in thatin a further process step

-   -   The scan points outside the aperture of the modulator cell are        set to zero,    -   A Fourier transformation of the complex amplitude transparency        is carried out to the Fourier plane in the far field,    -   The amplitude of the scan points in the preferred diffraction        orders or sections thereof in the far field is set to a value        which corresponds with the square root of the predefined        intensity value at that scan point, and    -   A Fourier back-transformation of the complex values of the far        field is carried out to the plane of the light modulator.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be described in detail below with the help ofembodiments in conjunction with the accompanying drawings, where

FIG. 1 a is a schematic view of a holographic direct-view displaywithout apodisation mask according to the prior art,

FIG. 1 b is a schematic view of a holographic direct-view display withapodisation mask according to this invention,

FIG. 2 is a graphic representation of the amplitude profile of anapodisation function for a modulator cell for the homogeneous reductionof diffraction orders starting with the ±2^(nd) order,

FIG. 3 is a graphic representation of the intensities in individualdiffraction orders in the Fourier plane, computed with and withoutiteration steps,

FIG. 4 is a graphic representation of the intensities in the Fourierplane for a cosine-shaped apodisation function and for a reduction ofnegative diffraction orders only, computed iteratively,

FIG. 5 is a graphic representation of an amplitude profile of acosine-shaped apodisation function and of the amplitude profile of theiteratively computed complex-valued apodisation function across amodulator cell according to FIG. 3,

FIG. 6 is a graphic representation of a phase profile of an apodisationfunction of complex values across a modulator cell according to FIG. 3,

FIG. 7 is a graphic representation of the intensities in the Fourierplane for a reduction of a region of negative and positive diffractionorders,

FIG. 8 is a graphic representation of an amplitude profile of anapodisation function across a modulator cell according to FIG. 6,

FIG. 9 is a schematic view of an embodiment of an array of apodisationmasks where all modulator cells have the same apodisation function,

FIG. 10 is a schematic view of an embodiment of an array of apodisationmasks where two groups of modulator cells are given which have differentapodisation functions, and

FIG. 11 is a schematic view which illustrates the reduction of preferreddiffraction orders in a two-dimensional diffraction pattern.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to a holographic direct-view display withat least one controllable spatial light modulator which comprisesmodulator cells 7′ 7″ which are arranged in a matrix 7, and where eachmodulator cell 7′, 7″ is assigned to an apodisation mask 6′, 6″ whichhas an apodisation function. The light modulator modulates the phaseand/or amplitude of sufficiently coherent light. The phase and/oramplitude values which are encoded on the light modulator can forexample represent a hologram which serves to reconstruct athree-dimensional object in a holographic direct-view display. Variouscombinations of light modulator and apodisation masks are possible. Forexample, a light modulator which modulates the phase only can becombined with an apodisation mask which apodises the amplitude only, andvice versa. Generally, both light modulator and apodisation mask can beused for a complex-valued modulation.

Determining the apodisation function for apodisation masks of modulatorcells according to this invention is based on the approach that—inaddition to the fix initial values—target values are defined forparameters to be set. Here, a complex amplitude shall specifically beset in the far field of the SLM which corresponds with the Fourier planeof the SLM. The complex amplitude is realised by way of a Fouriertransformation from the SLM to the far field.

Specifically, the parameter of luminous intensity in the Fourier planeis given. The luminous intensity shall be widely reduced in preferreddiffraction orders or just in a selected range of the preferreddiffraction orders. The shape of the active region of a modulator cellrepresents the position of the diffraction orders in the far field andthus in the Fourier plane. Since for example in a holographicdirect-view display the observer eyes are situated there as well,diffraction orders of the hologram which is encoded on the SLM and whichis intended for the left eye can hit the right eye and interfere withthe hologram which is intended for the right eye, and vice versa.

Thanks to the combination of modulator cells of the light modulator andapodisation mask, an apodisation function in an apodisation mask whichis computed with the respective parameters causes the incident light tobe modulated such that the intensity values in the Fourier plane comevery close to the intensity profile which is given there or which areidentical to that latter.

Another parameter for the apodisation function can be a phase functionwith constant amplitude. Other parameters in conjunction with the lightmodulation which are not specifically mentioned here can also beoptimised with the method according to this invention for determining anapodisation function for apodisation masks.

The target values can be approximated with the help of an iterativeprocess according to an embodiment of the present invention, thusoptimising the intensity profile.

The apodisation masks are designed as an array and are disposed ideallyas close as possible to the light-modulating optical layer of at leastone SLM. The array is either disposed directly on at least one SLM as anadditional front or rear layer or integrated into the cover glass of theat least one SLM. Further, the division bars between the active regionsof a modulator cell can already be designed such that they have theeffect of an apodisation array. The apodisation masks are aligned withthe given arrangement of modulator cells.

According to an embodiment, in addition to the SLM on which e.g.hologram values of a 3D scene are encoded, the holographic direct-viewdisplay can comprise a prism array which comprises electrowetting cellsas a further SLM which preferably modulates a wave front in itsdirection of propagation, but which can also modulate the phase and/oramplitude of that wave front.

FIG. 1 a shows schematically a top view of a holographic direct-viewdisplay according to the prior art, i.e. without apodisation mask. Thenumeral 1 denotes a holographic display device, 2 l and 2 r denote thereconstruction beams of an object point 5 of a three-dimensional scene,3 l and 3 r denote the visibility regions, also referred to as observerwindows, for a respective left and right observer eye in the far fieldof the display device 1, and 4 denotes the intensity distribution in thevisibility region 3 r for the right observer eye. The intensitydistribution 4 of the reconstruction beam 2 r also shows the occurringhigher diffraction orders, which cause cross-talking, thus adverselyaffecting the left observer eye.

FIG. 1 b shows schematically a top view of a holographic direct-viewdisplay according to this invention with an array of apodisation masks 6on the display device 1. The reconstruction beam 2 r of the object point5 generates in the visibility region 3 r for the right observer eye anintensity distribution 4′. At the position of the left observer eye thehigher diffraction orders of this intensity distribution 4′ are reducedsuch that they do not disturb the other observer eye.

FIG. 2 is a graphic representation which shows an apodisation functionwhich can be realised in an apodisation mask for a modulator cell. Thisapodisation function uniformly reduces diffraction orders starting withthe ±2^(nd) order of diffracted light according to a target. Theexemplary computation was only performed for one dimension in thisFigure. Generally, the areal extent of the modulator cell in twodimensions must be considered in the computation. In the example, themodulator cells are assumed to have a rectangular shape and thus toexhibit a rectangular transmittance curve.

For computing the apodisation function it is important to know thedistance between two adjacent modulator cells of the light modulator.This allows the location of the diffraction orders to be found preciselyin a matrix of modulator cells, in particular if only individual higherdiffraction orders are to be reduced. Knowing the distance is lessimportant if the intensities are to be reduced in contiguous ranges ofneighbouring diffraction orders.

At a defined position at a distance D from the light modulator, adiffraction order has the extent D·λ/p in one dimension, where λ is thewavelength of the light and p is the distance (pitch) between thecentres of two adjacent modulator cells of the same given group in thatdimension.

FIG. 3 shows the diffraction pattern of a single modulator cell with andwithout apodisation mask in the Fourier plane of the light modulator,where the amplitudes are shown on a logarithmic scale.

Curve K1 shows the diffraction pattern which is computed withoutapodisation as a sinc function for a rectangular transmittance which isconstant across the aperture of the modulator cell. Such a transmittanceprofile where the amplitude is set to the value 1 at all scan pointswithin the aperture of the modulator cell is also used as the initialvalue for the iterative process with which curve K2 was computed. In amodulator cell with an aperture which is as large as the cell distance,the distance between two minima of the sinc function would correspondwith the extent of a diffraction order. If the aperture is smaller thanthe cell distance, the diffraction orders are smaller by the same ratioof aperture and cell distance.

The curve K2 shows an amplitude profile in the Fourier plane which wascomputed with the help of the iterative process, resulting from theapodisation function of FIG. 2. The iterative process was terminatedafter five iteration steps and the result was used in the computation ofthe apodisation function.

The relative intensities of the higher diffraction orders of K2—in thediagram left and right of the central lobe—are clearly reduced comparedto K1.

Because here a symmetrical reduction of the positive and negativediffraction orders was stipulated, the result of the computation is adistribution of real amplitude or intensity values in the apodisationfunction.

This apodisation function can be realised in a first embodiment of anapodisation mask for uniform reduction of higher diffraction orders. Theresult of the computation is qualitatively similar to the curve whichwould be obtained with conventional analytical apodisation functions.The example shows that the iterative process can also be applied to ageneral case. The advantages of using the iterative process formodifying an apodisation function will become even clearer in the secondembodiment.

The diagrams in FIGS. 4 to 6 illustrate a second embodiment of anapodisation mask in which an apodisation function is realised which onlyreduces negative diffraction orders.

An application of such an embodiment would be a holographic direct-viewdisplay with a light modulator where one group of modulator cells areused for the generation of a visibility region for the left eye andanother group of modulator cells are used for the generation of avisibility region for the right eye.

In a light modulator of a holographic display for generating areconstruction, the Fourier plane is at the same time the plane wherethe visibility region is situated in which the reconstruction isvisible. Cross-talking of the left visibility region to the right eye isthen e.g. only affected by the intensity in preferred positivediffraction orders of the respective group of modulator cells.Cross-talking from the right visibility region to the left eye is onlyaffected by negative diffraction orders of the other group of modulatorcells, so that only the negative diffraction orders of that other groupmust be reduced.

FIG. 4 shows the amplitude profiles of the diffraction pattern in theFourier plane scaled to 1 for a reduction of diffraction orders with acosine-shaped curve of the apodisation function (curve K3) and theresult of the iterative computation with a reduction only of negativediffraction orders (curve K4).

The intensity profile of curve K4 was computed with iteration steps.This reduces the negative higher diffraction orders about as well aswith the cosine-shaped apodisation function. The positive higherdiffraction orders are about as high as in the diffraction pattern ofthe rectangular transmittance profile without apodisation, i.e. of thesinc function K1 in FIG. 3.

As regards the remaining intensity in the higher diffraction orders,using only the negative diffraction orders does not show any advantagein this embodiment. The advantage will only become clear when theapodisation profile in the modulator cell is considered which causes therespective reduction of negative orders.

FIGS. 5 and 6 are graphic representations of an amplitude profile and ofa phase profile of an apodisation function of complex values across amodulator cell according to FIG. 4.

FIG. 5 shows in addition to the curve M4 of the amplitude profile ofcomplex values the amplitude profile of a cosine-shaped apodisation ascurve M3. In this cosine-shaped apodisation, the phase is constantacross the modulator cell. The amplitude profile of the cosine-shapedapodisation function causes light to be absorbed in the marginal areasof the modulator cell. Altogether, an apodisation mask which is providedwith this apodisation function clearly reduces the total transmittanceof a modulator cell. It is 50% if the apodisation is only carried out inone dimension, and 25% in the case of a two-dimensional cosineapodisation. The 50% correspond with the mean value of the squaredcosine (intensity=amplitude squared) between −π/2 and π/2. This reducesthe luminous intensity in the higher diffraction orders relative to thezeroth diffraction order, but the absolute intensity willdisadvantageously be reduced equally in all diffraction orders,including the zeroth one. This cannot be seen in FIG. 4. There, theamplitude profiles are normalised to 1 to facilitate the comparison ofthe reduction of higher orders.

In contrast, the transmittance with the apodisation function which isfound using the iterative process is much higher. Referring to FIG. 5,the amplitude of the curve M4 and thus the intensity is almost 1 in thecentral region of the modulator cell, and it declines slightly towardsthe edges.

The restriction to the reduction of negative higher diffraction ordersshows an about equally good result in these diffraction orders, butwithout the above-mentioned disadvantage of a substantial loss inintensity in the other used diffraction orders.

The resulting apodisation function is complex-valued, because thereduction of higher orders is not symmetrical to the zeroth order.

Due to the symmetrical behaviour of the diffraction orders, anapodisation function for the reduction of all positive higherdiffraction orders can be obtained without a new iterative process inthat the amplitude profile of the apodisation function is chosen to bethe same, but the phase profile is mirrored.

In a holographic direct-view display with a light modulator where onegroup of modulator cells is used for the generation of a visibilityregion for the left eye and another group for the right eye, theapodisation mask would have the amplitude profile as shown in FIG. 5,curve M4, for all modulator cells. As regards the phase profile,however, one group of modulator cells would have the profile as shown inFIG. 6, and the other group would have a phase profile which is mirroredto this phase profile.

It becomes apparent from what has been said above that the modifiedprofile of the apodisation function cannot be described simply by oneequation. The second embodiment shows that the method can be usedgenerally in applications where no analytic apodisation functions areknown.

A further optimisation of the apodisation function is possible if notall positive or all negative higher diffraction orders are reduced, butonly preferred diffraction orders. In the holographic direct-viewdisplay discussed here, these are preferably those diffraction orderswhich hit the neighbouring eye.

Which orders are embraced by this definition depends on parameters likethe cell distance (pitch) of the modulator cells and the preferredobserver distance to the display. The affected orders can for example bethe +3^(rd) and +4^(th) or the −3^(rd) and −4^(th) diffraction order.

In a holographic direct-view display where the modulator cells are notfixedly assigned with the left or right eye, it can make sense tocompute the apodisation function such that preferred orders such as the+3^(rd) and +4^(th) or the −3^(rd) and −4^(th) diffraction order arereduced in the same way for all modulator cells. This applies forexample to holograms which are displayed sequentially to the left andright eye. Alternatively, it applies to an observer tracking feature ina display which assigns a certain modulator cell to the left eye for oneobserver position and to the right eye for another observer position.Cross-talking to the respective other eye can then be reduced on eitherside with the same modulator cells.

Such an apodisation function has advantages over the uniform reductionof all higher diffraction orders.

FIG. 7 shows the amplitude profile K5 normalised to 1 of the diffractionpattern in the Fourier plane for a reduction of a region of preferreddiffraction orders (indicated by arrows in the diagram). Here, thereduction is better than with a cosine-shaped apodisation by the curveK3 in FIG. 4.

FIG. 8 shows the amplitude profile of curve M5 over a modulator cellaccording to FIG. 7. Because of the symmetrical profile, the apodisationfunction is here real-valued again. The phase is also constantly zero.

With a transmittance of about 62% relative to a modulator cell withoutapodisation mask, the transmittance is higher than in the case of acosine-shaped apodisation, where it would amount to about 50% only.

In other applications, the iterative computation—with an accordingdefinition of target values—can also yield an increase in the intensityvalues of preferred diffraction orders.

FIG. 9 shows schematically a detail with regularly arranged modulatorcells 7′, 7″ of a light modulator, each of which being assigned with anapodisation mask 6′, 6″ with a one dimensionally computed apodisationfunction. One-dimensional here means that the amplitude and phase valuesof the apodisation function only change in one direction, herehorizontally, and are the identical in the orthogonal direction, herevertically, for different positions in the modulator cell 7′, 7″.Further, in this example there is only one group of modulator cells,this means that all modulator cells 7′, 7″ have the same apodisationfunction.

The diagram in FIG. 10 shows schematically a detail with regularlyarranged modulator cells 7′, 7″, which form two groups of modulatorcells.

The apodisation mask 6′, 6″ comprises for both groups a differentapodisation function which is additionally always computedtwo-dimensionally.

These groups of modulator cells can be used for different purposes, andthe apodisation function is computed separately for each group.

Two-dimensional here means that the amplitude and phase values of theapodisation function change in two directions, horizontally andvertically, in the modulator cell.

FIG. 11 shows schematically the diffraction pattern of a squaremodulator cell as a greyscale profile in two dimensions, which isrealised by a two-dimensional apodisation function. The relativebrightness is shown in a non-linear way. This diagram serves as anexample for a reduction of a range of preferred diffraction orders.

Similar to FIG. 10, only those diffraction orders are reduced whichwould fall on the right or left neighbouring eye if the other eye issituated in the zeroth diffraction order in a holographic direct-viewdisplay. The range of reduced diffraction orders is also confinedvertically, which is shown in the form of the two black rectangles inthe drawing. This result is achieved with an apodisation function whichhas a transmittance of about 77%.

Another example of the application of groups of modulator cells withdifferent apodisation functions is the presentation of 3D objects incolour.

In many types of light modulators, a coloured representation is achievedby way of spatial interleaving of modulator cells of different primarycolours, which are for example obtained with the help of red, green orblue colour filters. With such spatial interleaving of colours, themodulator cells of each primary colour form a given group, wheredifferent apodisation functions are found for each of those groups.

If a coherent illumination is used, it must be noted when finding theapodisation function that the width of a diffraction order changes inproportion with the wavelength.

In a holographic direct-view display with visibility regions for theleft/right eye, where the disturbing cross-talking between the twovisibility regions is to be prevented with the help of an apodisationmask, the higher diffraction orders for red, green and blue light havedifferent positions in relation to the neighbouring eye. To achieve asubstantial reduction of the diffraction orders, the apodisationfunction must therefore be computed separately with different set-pointvalues in the Fourier plane for the groups of modulator cells of eachindividual colour.

The division of the modulator cells of a light modulator in colourgroups can be combined with other systems of group divisions. If in a 3Ddisplay modulator cells are additionally fixed assigned to the left orright eye, then those modulator cells for red light and left eye canform one group for which an apodisation function is found, for example.

It is a further advantage of this invention that for finding anapodisation function for a group of modulator cells or for at least onelight modulator in the holographic direct-view display an iterativeprocess is carried out only once offline in a computing unit. Incontrast to other applications of iterative algorithms, thecomputational load and the required computing time do not play a rolethen.

Now, a method for determining an optimised apodisation function forapodisation masks which are assigned to regularly arranged modulatorcells of a spatial light modulator will be described, said methodincluding an iterative process.

First, intensity values are defined to serve as set-point values inpreferred diffraction orders or sections thereof for a defined positionin the optical path for carrying out an iterative process.

After having defined an apodisation function as an initial apodisationfunction, with the help of the known shape and size of a modulator cellof the given group of modulator cells the transmittance profile of themodulator cell is represented by a number of scan points in a gridinside and outside the modulator cell. A transmittance profile isgenerally understood to be an amplitude profile or an amplitude andphase profile in the form of complex values.

The grid of these scan points can be matched to the resolution withwhich a transmittance profile is technologically feasible to be madeacross a modulator cell if the point resolution of the manufacturingprocess is limited. Ideally, an analogue transmittance profile isgenerally desired.

For example, a modulator cell with a size of 60×60 μm where thetransmittance profile is to be realised with a resolution of 1 μm can berepresented by 60 scan points in each dimension.

If it is technologically feasible to manufacture a continuoustransmittance profile, the latter can still be approximated in thecomputation by scan points.

The scan points which represent the transmittance profile within themodulator cell are given initial phase and amplitude values. In the mostsimple case, this can be a rectangular function with the transmittanceof 1 within the aperture of the modulator cell, or any other knownanalytical apodisation function.

There is no transmittance outside the aperture of the modulator cell,which is why scan points which are situated there are set to zero. Aninitial apodisation function is provided with the given initial values,and this function is optimised with the help of an iterative process. Itis in particular the distribution of intensity values in the Fourierplane of the light modulator which is optimised.

The phase and amplitude values are transformed from the plane of thelight modulator to its Fourier plane, whereby the Fourier plane is givena distribution of amplitude values or complex values over multiplediffraction orders.

Since the computation is performed with the help of a Fouriertransformation, the number of diffraction orders in the Fourier planewhich are computed corresponds with the number of scan points within themodulator cell (aperture and cell margins), and the number of complexvalues within a diffraction order in the Fourier plane corresponds withthe ratio of total number of scan points and scan points within amodulator cell.

In the Fourier plane, the amplitude values or complex values arereplaced by set-point values in the given diffraction orders or sectionthereof, and in the remaining diffraction orders the above-mentionedvalues are taken from the transformation and back-transformed to theplane of the light modulator.

In the plane of the light modulator, the amplitude values or complexvalues within the aperture of the modulator cells which are computed byway of back-transformation are carried forward to the next iterationstep, and the amplitude values or complex values which lie outside theaperture of the modulator cells are set to zero.

Now, another iteration step with a transformation of the given values tothe Fourier plane can be started.

The iterative process is either terminated after a predefined number ofiteration steps, or when another predefined termination criterion issatisfied.

It is for example possible to compare the setpoint values in higherdiffraction orders with the actual values in the Fourier plane before areplacement as a termination criterion. The iteration will be terminatedif the deviations of the actual values from the setpoint values fallsbelow a certain threshold. Complex values which are the computed resultof a Fourier transformation between the plane of a light modulator andits Fourier plane in one iteration step in one of these two planes arereferred to as actual values here.

It is possible to introduce further conditions for the cycle of theiterative process. For example, it is possible to specify that theamplitude and phase values are quantised within the modulator cell, andthat those quantised values are used for the apodisation function whichhave the smallest difference to the respective actual value instead ofcarrying over actual values in each iteration step for the scan pointsin the modulator cell.

For this, the amplitudes of the actual values are preferably normalisedsuch that their range of values matches that of the quantised values. Anormalisation to a range of between 0 and 1 can be achieved with thehelp of a division by the maximum amplitude.

Such a computation of a quantised apodisation function is particularlysensible if the apodisation function is computed in the context of acertain manufacturing process of the apodisation mask and if only alimited number of different greyscale values or phase values can berealised with that method. A special case of it is a binary apodisationmask which only contains black and fully transparent sections, i.e. twoquantisation steps.

In another modification of the method, it can be specified that theapodisation function is a phase-only function. A phase function has theadvantage that the transmittance of the light modulator is not reducedby the apodisation mask. For a phase function, the phase part of acomplex-valued actual value is taken over and its absolute value is setto 1 at the scan points within the aperture of the modulator cell ineach iteration step.

For reducing only negative or only positive orders, it is for examplepossible to use a phase-only function. Although it delivers remainingintensity values which are somewhat higher in these diffraction ordersin contrast to the curve K4 in FIG. 4, this result is achievedcompletely without any reduction in transmittance of the lightmodulator.

Another option for the termination criterion is to set the amplitude toa minimum value.

According to a certain method for manufacturing an apodisation mask, itmakes sense to choose the scan points for the computation depending onthe size of the modulator cell such that their distance eithercorresponds with the spatial resolution of that mask or is slightlylarger, so that the apodisation mask can be made by way of interpolationbetween the scan points.

The advantage of an iterative process for determining the apodisationfunction is that an apodisation function which is optimised to thespecific application can be computed and realised in an apodisationmask. In contrast, standard apodisation functions only allow a generalreduction of the light intensity uniformly in all higher diffractionorders, where the reduction in intensity typically outweighs theintensity which is optimised for a certain higher diffraction order.

Moreover, the reduction in transmittance of the light modulator is lowerwhen using the apodisation function which is optimised to a certainapplication than when using a standard apodisation function.

The apodisation masks which are provided with the determined apodisationfunction realise the desired amplitude transparency in the controllablelight modulator and thus a reduction of higher diffraction orders. Thislight modulator can be used in a holographic direct-view display withvisibility regions in the Fourier plane which are assigned separately toa left/right eye, or in a stereoscopic display for the presentation ofspatial objects to observer eyes. In the latter type of display, anillumination with coherent light would be essential. With the help ofthe apodisation function it is achieved that cross-talking between thevisibility regions of the stereo views between left and right eye isminimised.

If in the above-mentioned displays a spatial interleaving of visibilityregions is realised which are generated at a defined distance to theobserver, and if the modulator cells are fixedly assigned to a left orright observer eye, then groups of modulator cells can be specified suchthat the diffracted light of each group generates visibility regions inthe Fourier plane which are assigned to the respective observer eyes.The set luminous intensity of the one group is minimised at a givenobserver distance at the observer eye of the other group and vice versa.In this case, the modulator cells for the left observer eyes exhibit anapodisation function which differs from that of the modulator cells forthe right observer eyes.

For modulator cells of a controllable light modulator, apodisation masksare designed with which the light modulator can preferably realise anindividually specified intensity distribution in the diffraction ordersof diffracted coherent light. For this, an apodisation function for theapodisation masks was determined, where target values of luminousintensities in given higher diffraction orders must be considered of ina simplified manner in the computation. It is technologically feasiblethat the thus modified apodisation function is realised in anapodisation mask. Further, it is possible either to give the apodisationfunction a continuous profile or to realise an apodisation function withdiscrete values in single steps across the modulator cell in theapodisation mask.

This invention also allows to use such amplitude and/or phase profilesin modulator cells as apodisation functions which cannot be described byan analytical function.

The apodisation is here preferably made possible with simple functions(cosine etc.) or, in the most simple case, with binary steps. Further,disturbing margin effects in modulator cells can be weakened by anapodised intensity or phase profile in that for example the margin ofthe modulator cell is darkened or cut off. This also allows thereconstruction quality to be improved in the visibility region itself.

The invention can be applied both in modulators with liquid crystalcells and in modulators with electrowetting cells or other types ofcells. The SLM and thus the holographic or autostereoscopic displays caneither be of a reflective or of a transmissive type. The displays whichare described in this invention are direct-view displays.

In the case MEMS-based reflective piston micro-mirror arrays are used asSLMs, an array of apodisation masks can be realised in that a modulatorcell is given a reflectivity gradient.

The invention claimed is:
 1. Holographic direct-view display, comprisingAt least one controllable spatial light modulator with a matrix ofmodulator cells for diffracting light, said spatial light modulatorrealising an individually predefined intensity profile in the far fieldof the light modulator, An array of apodisation masks, where eachmodulator cell for modulating the phase and/or amplitude of sufficientlycoherent light is assigned to an apodisation mask, At least one definedgroup of modulator cells which are assigned to apodisation masks with anidentical apodisation function, and A complex amplitude transparencywhich is set for the at least one group of modulator cells and whichsets the apodisation function for this group of modulator cellsaccording to the predefined intensity profile which is to be realised,where the predefined intensity profile includes a reduction in theluminous intensity in at least one higher diffraction order and/or ofthe stray light which is emitted by the light modulator.
 2. Holographicdirect-view display according to claim 1, wherein the apodisationfunction exhibits at least in one dimension a non-constant profile ofthe absolute value and/or phase of the complex amplitude transparency.3. Holographic direct-view display according to claim 2, wherein theapodisation function has a maximum in the centre of a modulator cell,and a gradually decreasing complex amplitude transparency towards theedges of a modulator cell.
 4. Holographic direct-view display accordingto claim 2, wherein the apodisation function is computed depending onthe given shape, size and geometry, and on an already inherent complexamplitude transparency of a modulator cell.
 5. Holographic direct-viewdisplay according to claim 1, wherein the apodisation function isdefined at discrete scan points by numerical values which describe thecomplex amplitude transparency at those scan points, where the scanpoints exhibit a mutual distance which is spatially resolvable by theapodisation mask.
 6. Holographic direct-view display according to claim1, wherein at least two controllable light modulators are sandwichedtogether, where either each light modulator has a dedicated apodisationmask or the at least two light modulators have a common apodisationmask.
 7. Holographic direct-view display according to claim 1, whereinthe apodisation masks of the given group of modulator cells set anintensity profile with predefined intensity values in a given section ofthe far field of the diffracted light.
 8. Holographic direct-viewdisplay according to claim 7, wherein the given section of the far fieldcomprises either only negative or only positive diffraction orders in atleast one dimension.
 9. Holographic direct-view display according toclaim 1, wherein all modulator cells have identical apodisationfunctions.
 10. Holographic direct-view display according to claim 1,wherein modulator cells are assigned to either a left or right observereye, and where modulator cells form given groups of modulator cells forgenerating visibility regions which are respectively assigned to thoseobserver eyes in an observer distance range to the light modulator,where the intensity profile of the one group which is set with the helpof the apodisation mask is minimised at the position of the observer eyeof the other group and vice versa.
 11. Holographic direct-view displayaccording to claim 1, wherein the apodisation mask exhibits anapodisation function whose complex amplitude transparency is formed as avariable phase function with constant absolute value, or where theapodisation mask exhibits an apodisation function whose complexamplitude transparency is formed as a variable phase function withconstant absolute value, and where the apodisation mask exhibits anapodisation function whose complex amplitude transparency is of a binarytype, so to reduce preferably stray light.
 12. Holographic direct-viewdisplay according to claim 1, wherein for determining the apodisationfunction an iterative process is used which is run as a computingroutine in a computing unit, and which provides the result in a memoryunit for being retrieved.
 13. Holographic direct-view display accordingto claim 12, wherein the iterative process includes a Fouriertransformation where the transform is carried out between the plane ofthe light modulator and its Fourier plane in the far field, where thelight which is diffracted at the modulator cells can be approximated togiven intensity values in the given section of the far field. 14.Holographic direct-view display according to claim 1, wherein theapodisation mask is an amplitude mask which can be manufactured by wayof projection-lithographic, interference-lithographic orgreyscale-lithographic methods.
 15. Holographic direct-view displayaccording to claim 1, wherein the apodisation mask is a phase mask whichcan be manufactured by way of generating surface profiles or refractiveindex modulation in polymers or glass substrates.
 16. Holographicdirect-view display according to claim 1, wherein those modulator cellswhich are assigned to respectively one primary colour form a given groupof modulator cells.
 17. Holographic direct-view display according toclaim 16, wherein the given section of the far field includes a range ofidentical diffraction angles for all primary colours for minimising theintensity values.
 18. Method for determining an apodisation function forapodisation masks which are arranged in an array and which are assignedto a matrix of modulator cells of a controllable spatial light modulatoraccording to claim 1, wherein the method is carried out in iterativeprocess steps.
 19. Method according to claim 18, comprising thefollowing process steps: Determining the position of diffraction ordersof the modulator cells of a given group, Definition of an individuallypredefined intensity profile in preferred diffraction orders or sectionsthereof in the far field, Definition of an initial apodisation functionfor a single modulator cell of the given group, and Stepwiseoptimisation of the complex amplitude transparency of the apodisationfunction to approximate to the predefined intensity profile in thepreferred diffraction orders of sections thereof in the far field. 20.Method according to claim 19, wherein the complex amplitude transparencyof a modulator cell is determined by defining a number of scan pointsinside and outside the aperture of the modulator cell, where theintensity profile in the far field is determined by the square absolutevalue of the Fourier transform of the complex amplitude transparency atan identical number of scan points, where the stepwise optimisation ofthe complex amplitude transparency of the apodisation function takesplace in that in a further process step The scan points outside theaperture of the modulator cell are set to zero, A Fourier transformationof the complex amplitude transparency is carried out to the Fourierplane in the far field, The amplitude of the scan points in thepreferred diffraction orders or sections thereof in the far field is setto a value which corresponds with the square root of the predefinedintensity value at that scan point, and A Fourier back-transformation ofthe complex values of the far field is carried out to the plane of thelight modulator.